Re: [Gretl-users] Standard error for confidence intervals
On Viernes, 16 de Octubre de 2009 13:15:56 Francisco Sosa escribió:
Actually my model is:
Y'_t=alpha+beta X'_t + E_t
When Y'_t= Y_t - rho*Y_t-1 and X'_t= X_t - rho*X_t-1.
And E_t=rho*E_(t-1)+U_t is the standard formula for one AR(1).
Prais-Winsten is an improvement of the algorithm for estimating regressions
(AR(1)) in the present of autocorrelated errors, I guess I have to do
something else to calculate the E_t+h, I need the variance to calculate the
confidence interval.
Prais-Winsten is a type of feasible GLS estimator. I don't know the formula
that gretl uses for the static forecasts but I assume it is the standard one
that can be found in any econometric book. I also would like to know what
gretl does when selecting "dynamic" forecast.
Having a look at the gretl source code for "forecast", I think the relevant
comment in forecast.c is this below, but is not of much help for me, is it for
you?
/*
The code below generates forecasts that incorporate the
predictable portion of an AR error term:
u_t = r1 u_{t-1} + r2 u_{t-1} + ... + e_t
where e_t is white noise. The forecasts are based on the
representation of a model with such an error term as
(1 - r(L)) y_t = (1 - r(L)) X_t b + e_t
or
y_t = r(L) y_t + (1 - r(L)) X_t b + e_t
where r(L) is a polynomial in the lag operator.
We also attempt to calculate forecast error variance for
out-of-sample forecasts. These calculations, like those for
ARMA, do not take into account parameter uncertainty.
This code is used for AR and AR1 models; it is also used for
dynamic forecasting with models that do not have an explicit AR
error process but that have one or more lagged values of the
dependent variable as regressors.
*/
--
Ignacio Diaz-Emparanza
DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA)
UPV/EHU
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